Estate Taxation, Entrepreneurship, and Wealth∗

Marco CagettiBoard of Governors, Federal Reserve System

Mariacristina De NardiFederal Reserve Bank of Chicago and NBER

Abstract

We study the effects of abolishing estate taxation in a quantitativeand realistic framework that includes the key features that policy makersare worried about: business investment, borrowing constraints, estatetransmission, and wealth inequality. We use our model to estimate effec-tive estate taxation. We consider various tax instruments to reestablishfiscal balance when abolishing estate taxation. We find that abolish-ing estate taxation would not generate large increases in inequality, andwould, in some cases, generate increases in aggregate output and capitalaccumulation. If, however, the resulting revenue shortfall were financedthrough increased income or consumption taxation, the immensely rich,and the old among those in particular, would experience a welfare gain,at the cost of welfare losses for the vast majority of the population.

∗We gratefully acknowledge financial support from NSF grants (respectively) SES-0318014 and SES-0317872. De Nardi also thanks the University of Minnesota Grant-in-Aidfor funding. We are grateful to Gadi Barlevy, Marco Bassetto, Luca Benzoni, Jeff Campbell,Robert E. Lucas, Ellen McGrattan, Kulwant Rai, Ivan Werning, an editor, three anonymousreferees, and to seminar participants at many institutions for helpful comments. The viewsherein are those of the authors and not necessarily those of the Federal Reserve Bank ofChicago, The Federal Reserve Board, the Federal Reserve System, or the National ScienceFoundation.

1

1 Introduction

Since its introduction in 1916 the estate tax has been one of the most contro-

versial taxes in the United States tax code.

The estate tax opponents call it the “death tax”. Among the legislators

supporting the abolition of the estate tax, representative Ron Paul (14th dis-

trict of Texas) states: “The estate tax is immoral and counter-productive. ...

My office has received hundreds of letters and emails from individuals and

small business owners in my district. Theses people are not rich, but they

have worked hard and saved to create an inheritance for their children...” Sen-

ator Patty Murray, from Washington State, states “I believe that we need to

repeal the estate tax. It is bad for businesses. It’s bad for workers and new job

creation.” President George W. Bush shares this view “The death tax results

in unfair double taxation of income and it hurts America’s small businesses,

which are the engine of job creation.”

The estate tax supporters see the estate tax as an extremely progressive

tax and a very effective effective way to tax the richest (and dead) few. Rep-

resentative Bart Stupak (1st district of Michigan) states “I have continuously

supported reforming the estate tax, but a complete repeal is fiscally irrespon-

sible, and serves to benefit only mega multi-millionaires while harming our

economy...”. Former Senator Tom Daschle, South Dakota adds “Do we really

have to protect the billionaires? We are talking about the richest 2%.” The

estate tax supporters thus seem to believe that reducing estate taxation is a

“Paris Hilton Benefit Tax Act,” meaning that reduced estate taxes only ben-

efit the heiresses and heirs of the largest fortunes in the country, rather than

benefiting small entrepreneurs and family businesses. They also point out that

the abolition of the “death tax” would imply replacing a tax on few rich and

2

dead people with a “birth tax” on all citizens.

This paper studies the effects of abolishing estate taxation using a model

that explicitly studies entrepreneurial entry, continuation decisions, investment

and job creation, and transmission of estates across generations. While cali-

brated to match some other key aspects of the data, this framework matches

the observed wealth inequality and wealth mobility for both entrepreneurs and

workers, and replicates the observed consumption inequality.

We use our framework to provide a measure of effective estate taxation

by matching aggregate estate taxes paid as a fraction of output and the frac-

tion of estates that pay estate taxes. Given that our model provides such a

good fit of observed net worth holdings, we argue that this is a good way to

measure effective estate taxation. We find that the current statutory estate

taxation code implies a large effective exemption level (about 5 million dol-

lars per household), and a fairly low effective marginal tax rate (16%). These

numbers are consistent with people rationally using legal exemptions, special

provisions, and favorable valuation methods to lower the estate tax burden,

and with previous estimates which used various other methods to estimate

the schedule for the effective estate tax (see Gale, Hines and Slemrod for an

overview [17]). They are also consistent with previous arguments according to

which the exemption level is high enough to imply that the impact of estate

taxes on family farms and businesses is not a major concern for most estates

(see for example Harl [24] and Gale and Slemrod [19]).

We use our calibrated model to evaluate the aggregate and distributional

effects of abolishing estate taxation. We compute the steady states before and

after abolishing estate taxes, and the transition path of the economy between

steady states. We consider alternative fiscal policies to reestablish fiscal bal-

ance when estate taxation is eliminated. First, we allow the government to

3

cut government spending. Since government spending is unproductive in our

framework, this should be the the scenario that is most favorable for abolish-

ing estate taxes. Second, the government increases the tax on consumption.

Third, the government increases the tax on total income.

We find that the effect of these policies on long-run inequality (both in

terms of consumption and wealth) is small.

In contrast, the steady state aggregate effects on output and capital are

positive and significant, compared to the small revenue raised by the estate

and gift taxes (which is about 0.3% of GDP) when either government spending

is cut, or when the tax rate on consumption is increased. Under those policies,

aggregate output goes up by 1%-1.5%, while aggregate capital increases by

2.5%. The aggregate effects are instead much smaller when the tax rate on

total income is increased. Even if the income tax increase required to make

up for the shortfall in estate taxes is very small, this increased tax burden

decreases the return from running a business. The majority of entrepreneurs

would hence run their productive technologies on a smaller scale, which would

imply smaller gains in aggregate output and capital.

These reforms have significant distributional implications. Looking at the

welfare implications for the individual households, unsurprisingly the reform in

which wasteful government spending is cut, is the reform that casts abolishing

estate taxation in the most favorable light. In that case, increased investment

by the entrepreneurs increases capital, and hence wages. Wages are the largest

source of income for most of the population, therefore most of the households

experience a welfare gain from this reform. The super-rich, and especially the

old, benefit from the reduction in estate taxation. The rich who were below

the estate taxation threshold before the reform, however, loose, because they

receive a large fraction of income as capital income, and the interest rate goes

4

down due to the increase in entrepreneurial savings and aggregate capital.

About 80% of the young and 90% of the old households benefit from this re-

form, with an average welfare gain of the order or 0.2% of yearly consumption.

The reforms in which either the consumption or the income tax is raised

to make up from the budget shortfall from abolishing estate taxation, instead,

generate small welfare costs (of at most 1% of yearly consumption) for the

vast majority of the population, while generating sizeable welfare gains for the

richest few, and for the richest old in particular (on the order of 6% of yearly

consumption). The average welfare costs of these reforms are about 0.2-0.3%

of yearly consumption.

Our results thus suggest that most households alive today would find in

their interest to oppose a reform in which a consumption or income tax were

raised to compensate for decreased revenues from abolishing estate taxation.

To the best of our knowledge this paper is the first work that evaluates

estate taxation reforms by using a quantitative, general equilibrium model

that takes into account the effects of the reforms on the key channels that

most worry legislators: wealth inequality, business activity, aggregate activity

at large, and estate transmission, and that quantitatively matches a number

of important features of the data, including wealth inequality.

Our findings are based on a life-cycle model with perfect altruism across

generations and period-by-period occupational choice. Some households have

the ability to employ capital and labor more productively than others, and po-

tential and existing entrepreneurs face borrowing constraints because contracts

are imperfectly enforceable.

This framework builds on Cagetti and De Nardi [11] by allowing the en-

trepreneurs to hire workers, by introducing progressive income and estate tax-

ation, proportional consumption taxation, and by computing the transition

5

paths of the economy in response to tax changes1.

Despite the relevance of estate taxation reforms and its big impact in the

policy circles, few papers study it in the context of quantitative models capable

of matching the extreme concentration of wealth observed in the data. This

is because constructing such a model, computing it, and calibrating it to the

data are not easy tasks (see Quadrini and Rıos-Rull [38] and Cagetti and De

Nardi [12] for a discussion.)

Castaneda, Dıaz-Gimenez, and Rıos-Rull [13] and Laitner [30] are excep-

tions in that they study estate taxation in the context of quantitative models

that are, to some extent, capable of matching the extreme concentration of

wealth observed in the data. Neither of these papers, however, model en-

trepreneurial business formation, job creation, and investment, which, accord-

ing to many legislators, is a a key channel affected by estate taxation.

Further supporting the importance of explicitly modeling entrepreneurship,

previous literature has shown that entrepreneurship is a key determinant of

investment, saving, wealth holdings, and wealth inequality (See Quadrini and

Rıos-Rull [39], Quadrini [36] and [37], Gentry and Hubbard [20], and Cagetti

and De Nardi [11]), and is important to evaluate the effects of some income

tax reforms (Meh [34], Kitao [27]).

Section 2 provides a brief overview of estate taxation in the United States.

Section 3 describes our model. Section 4 discusses our calibration procedure.

Section 5 evaluates the fit of our model against a number of important features

of the data that we do not match by construction. Section 6 evaluates the

effects of abolishing estate taxation while using various instruments to re-

establish fiscal balance, and section 7 concludes.

1See Conesa and Krueger [14] for an earlier example computing the economy’s transitionpath in a Beweley model.

6

2 A brief overview of estate taxation in the

United States

Among the most recent literature Gale, Hines, and Slemrod [17], Aaron and

Gale [1], and Gale and Perozek [18] provide overviews and discussions on estate

and gift taxation. Here we only focus on the features of both statutory and

effective estate taxation that are most important given our purposes.

Federal law imposes an integrated set of taxes on estates, gifts, and gener-

ation skipping transfers. The gross estate includes all of the decedent’s assets.

In the process of going from the gross estate to the net, taxable estate, there

are some of the important steps2:

1. The allowed estate tax implied exemption level was $675,000.

2. Assets are typically evaluated at fair market value. Closely held busi-

ness, however, are allowed to value real property assets at their “use

value” rather than their highest alternative market-oriented value. The

maximum allowed reduction in value was $770,000.

3. In addition, it is often possible to substantially discount asset value when

such assets are not readily marketable or the taxpayers’ ownership does

not correlate with control.

4. Interests in certain qualified family businesses were also allowed an extra

deduction of up to $ 625,000 in 2000 for the value of the business being

transferred.

2We focus on the characteristics of the 2000 tax code. See Johnson, Mikow, and BrittonHeller [8], and Brownlee [10] for a historic perspective on Federal Estate taxation.

7

5. One can apply unlimited deductions for transfers to a surviving spouse.

After determining the net estate, that is, the gross estate appropriately

valued less deductions, the statutory tax rate is applied. The “applicable credit

amount” implied that in 2000 at least the first $675,000 were not taxable. The

marginal federal tax rate for a taxable returns above that amount was starting

at 37% and topping out at 55%

Credit is given for state inheritance and estate taxes. Most states now levy

“soak-up taxes” that only shift revenues from the federal to the state treasuries

without adding to the total tax burden on the estate.

Just by looking at the simple scheme above, once can see that a rich couple

could immediately double the standard exemption level just by leaving the

children assets up to the deduction upon the death of the first decedent, and

then applying the deduction a second time upon death of the other spouse.

Judicious application of valuation schemes and extra deduction for the

presence of a family business further increase the exemption level and brings

down the effective estate tax rate above the exemption level. Schmalbeck [40]

describes many (legal) estate taxes avoidance schemes to reduce the estate tax

burden and provides some measures of effective estate taxes after such schemes

are implemented.

Gale and Slemrod [19] argue that simply by using legal valuation tech-

niques, exemptions, and various deductions, a couple with a $4 million dollar

business could pass it to their heir without paying any estate taxes, and without

having to engage in any complicated tax avoidance scheme. They also argue

that this threshold can be increased even further using other legal schemes.

Britton Eller, Erard, and Ho [33] focus on tax noncompliance by using

audit data. They find that overall (illegal) estate tax evasion to be about 13%

8

of the potential tax base.

Aaron and Munnell [2] and Kopczuk et al. [28] also argue that there are

many ways to reduce effective estate taxation.

Although many experts agree that effective estate taxation can be sub-

stantially reduced by appropriate estate management and valuation (this can

be done, in part, even after the death of the decedent), there is considerable

uncertainty about how much people can and do reduce the estate tax burden

by using both legal and illegal ways. Wolff [46] and Poterba [35] study this by

comparing tax revenues and the distribution of estates reported in tax forms

with the hypothetical one that would be implied by the Survey of Consumer Fi-

nances using mortality probabilities and many other assumptions. While Wolf

argues that the estate tax captures only about 25% of the potential tax base,

Poterba concludes that it catches most of it. Similarly, there is uncertainty

about the effective progressivity of the estate tax and on its exact exemption

level. Some argue that it is easier to decrease the tax burden for smaller es-

tates (which are also less likely to be audited). Others argue that given the

economies of scale for tax avoidance and evasion the tax burden might actually

be lower for larger estates.

There is, in contrast, no dispute about the observed revenues from the

estate and gift tax, and about the fraction of estates that do pay estate taxes.

In terms of revenue, only about 2% of the estates of adult decedents do pay any

estate taxes, and their revenue is about 0.3% of US output (See for example

Gale and Slemrod [19]).

In the process of calibrating our model we propose a complementary and

novel way to assess the burden of estate taxation. We assume a simple form

for estate taxation that allows for an exemption level and a constant tax rate

above such exemption level, and we use our model generated data to match the

9

fraction of estates paying estate taxes, and estate tax revenues as a fraction

of output. Interestingly, we find numbers that fall well within the bounds

proposed by the previous literature. Given that our model matches asset

holdings so well both for entrepreneurs and workers, and given the considerable

uncertainty about effective estate tax avoidance and evasion, we see this as a

useful way to proceed.

Legislation passed in 2003 has statutory marginal tax rates gradually de-

crease each year, and statutory exemption levels to gradually increase every

year until 2010. In 2010, all estates are be taxed at 0%. In 2011, however, these

temporary cuts are scheduled to vanish, and the statutory taxation schedule

is to revert to much higher levels. Many interpret this path as compelling

evidence that a reform is needed.

3 The model

Since we compute the transition dynamics between the steady states corre-

sponding to a given policy experiment, we make time subscripts explicit when-

ever relevant.

3.1 Demographics

We adopt a life-cycle model with intergenerational altruism. To make the

results quantitatively interesting, we need short time periods. To make the

model computationally manageable, we have to keep the number of stages

of life small. To reconcile these two necessities, we adopt a modeling device

introduced by Blanchard [9] and generalized by Gertler [21] to a life-cycle

setting.

10

Our model period is one year long. Households go through two stages of

life, young and old age. A young person faces a constant probability of aging

during each period (1 − πy), and an old person faces a constant probability

of dying during each period (1 − πo). When an old person dies, his offspring

enters the model, carrying the assets bequeathed to him by the parent.

Appropriately parameterized, this framework generates households for which

the average length of the working period and the retirement period is realistic.

There is a continuum of households of measure 1.

3.2 Preferences

The household’s flow of utility from consumption is given byc1−σt

1−σ. The house-

holds discount the future at rate β and are perfectly altruistic toward their

descendants.

3.3 Technology

Each person possesses two types of ability, which we take to be exogenous,

stochastic, positively correlated over time, and uncorrelated with each other.

Entrepreneurial ability (θt) is the capacity to invest capital and labor more or

less productively using one’s own production function. Working ability (yt) is

the capacity to produce income out of labor by working for others.

The entrepreneurs can borrow, invest capital, hire labor, and run a tech-

nology whose return depends on their own entrepreneurial ability: those with

higher ability levels have higher average and marginal returns from capital

and labor. When the entrepreneur invests kt production net of depreciation is

given by

f(kt, nt) = θ(kγt (1 + nt)

(1−γ))ν + (1 − δ)k

11

where ν, γ ∈ [0, 1], and n is hired labor (n ≥ 0). We normalize the labor of the

entrepreneur to 1. Entrepreneurs thus face decreasing returns from investment,

as their managerial skills become gradually stretched over larger and larger

projects (as in Lucas (1978)). While entrepreneurial ability is exogenously

given, the entrepreneurial rate of return from investing in capital is endogenous

and is a function of the size of the project that the entrepreneur implements.

There is no within-period uncertainty regarding the returns of the en-

trepreneurial project. The ability θt is observable and known by all at the

beginning of the period. We therefore abstract from problems arising from

partial observability, costly state verification, and from diversification of en-

trepreneurial risk.

Workers can save (but not borrow) at a riskless, constant rate of return.

Many firms are not controlled by a single entrepreneur and are not likely

to face the same financing restrictions that we stress in our model. There-

fore, as in Quadrini (2000), we model two sectors of production: one popu-

lated by the entrepreneurs and one by “non-entrepreneurial” firms. The non-

entrepreneurial sector is represented by a standard Cobb-Douglas production

function:

F (Kct , L

ct) = A(Kc

t )α(Lc

t)1−α (1)

where Kct and Lc

t are the total capital and labor inputs in the non-entrepreneurial

sector and A is a constant. In both sectors, capital depreciates at a rate δ.

3.4 Credit market constraints

As in Marcet and Marimon [32], Kehoe and Levine [26], Albuquerque and

Hopenhayn[3], Cooley, Marimon, and Quadrini [15], and Cagetti and De Nardi [11],

the borrowing constraints are endogenously determined in equilibrium and

12

stem from the assumptions that contracts are imperfectly enforceable.

Imperfect enforceability of contracts means that the creditors will not be

able to force the debtors to fully repay their debts as promised, but that the

debtors fully repay only if it is in their own interest to do so. Since both

parties are aware of this feature and act rationally, the lender will lend to a

given borrower an amount (possibly zero) that will be in the debtor’s interest

to repay as promised.

In particular, we assume that the entrepreneurs who borrow either can

invest the money and repay their debt at the end of the period or can run

away without investing it and be workers for one period. In the latter case,

they retain a fraction f of their working capital kt (which includes own assets

and borrowed money) and their creditors seize the rest. We assume that

labor services are paid at the end of the period, hence entrepreneurs are not

contrained in the amount of labor that they hire.

In the absence of market imperfections, the optimal level of capital is

only related to technological parameters and does not depend on initial as-

sets. In our framework, instead, the higher the amount of the entrepreneur’s

own wealth invested in the business, the larger the amount that the borrower

would lose in case of default. Hence, the lower the incentive to default, and the

larger the sum that the creditor is willing to lend to the entrepreneur. Hence,

the entrepreneur’s assets act as collateral, but the loan is not necessarily fully

collateralized.

As a result, not all potentially profitable projects receive appropriate fund-

ing. Households with little wealth can borrow little, even if they have high

ability as entrepreneurs. Since the entrepreneur forgoes his potential earnings

as a worker, he will choose to become an entrepreneur only if the size of the

firm that he can start is big enough, that is, if he is rich enough to be able to

13

borrow and invest a suitable amount of money in his firm.

3.5 Government and taxation

The government is infinitely lived. It levies taxes, pays a pension pt to each

retiree, provides a certain level gt of public purchases (which do not enter

the households’ utility function), and pays interest on the accumulated debt.

During every period, tax revenues from income, consumption, and estate taxes

are equal to government purchases, pension payments, and interest payments

on the debt.

We model progressive taxation of total income (as in Altig and Carl-

strom [5]), and we allow the tax schedules to be different for entrepreneurs

and non-entrepreneurs (including workers and retirees). We adopt Gouveia

and Strauss’ [23] functional form and assume the average federal tax rate

τ i(Yt) on total income Yt is given by

τ i(Yt) = bi − bi(siYpi

t + 1)−

1

pi , (1)

where i = e, w: entrepreneurs and workers. Gouveia and Strauss [23] have

shown that this functional form is flexible enough to approximate well the

effective average tax rate. As explained in the calibration section, we esti-

mate the parameters bi, si, and pi from microeconomic data, separately for

entrepreneurs and non-entrepreneurs.

Total income taxes paid by each household are given by

T it (Yt) = τ i(Yt)Yt + τ s

t Yt,

where τ st captures state and other income taxes (other than federal). The

14

government also levies a sales tax on consumption, at rate τ ct . Estates larger

than a given value et are taxed at rate τ bt on the amount in excess of et. The

tax rates τ st , τ c

t , and τ bt are potentially time-varying, depending on the policy

experiment under consideration.

3.6 Households

At the beginning of each period the current ability levels are known with

certainty, while next period’s levels are uncertain. Each young individual starts

the period with assets at, entrepreneurial ability θt, and worker ability yt and

chooses whether to be an entrepreneur or a worker during the current period.

An old entrepreneur can decide to keep the activity going or retire, while

a retiree cannot start a new entrepreneurial activity.

The young’s problem

The value function of a young person is

Vt(at, yt, θt) = max{V et (at, yt, θt), V

wt (at, yt, θt)}, (2)

where V et (at, yt, θt) is the value function of a young individual who manages

an entrepreneurial activity during the current period. The term V wt (at, yt, θt)

is the value function if he chooses to be a worker during the current period.

The young entrepreneur’s problem can be written as

V et (at, yt, θt) = max

ct,kt,nt,at+1

{u(ct)+βπyEtVt+1(at+1, yt+1, θt+1)+β(1−πy)EtWt+1(at+1, θt+1)}

(2)

15

subject to

Y et = θ(kγ

t (1 + nt)(1−γ))ν − δkt − rt(kt − at) − wtnt (3)

at+1 = Y et − T e

t (Y et ) + at − (1 + τ c

t )ct (4)

u(ct)+βπyEtVt+1(at+1, yt+1, θt+1)+β(1−πy)EtWt+1(at+1, θt+1) ≥ V wt (f ·kt, yt, θt)

(5)

at ≥ 0 (6)

nt ≥ 0 (7)

kt ≥ 0. (8)

The term Y et represents the entrepreneur’s total profits. The expected

value of the value function is taken with respect to (yt+1, θt+1), conditional on

(yt, θt). Eq. (5) determines the maximum amount that an entrepreneur with

given state variables can borrow. The term Wt(at+1, θt+1) is the value function

of the old entrepreneur at the beginning of the period, before deciding whether

to stay in business or retire. We have

V wt (at, yt, θt) = max

ct,at+1

{u(ct)+βπyEtVt+1(at+1, yt+1, θt+1)+β(1−πy)Wrt+1(at+1)}

(9)

subject to eq. (6) and

Y wt = wt yt + rt at (10)

at+1 = (1 + rt)at − Twt (Y w

t ) − (1 + τ ct )ct, (11)

where wt is the equilibrium wage rate.

16

The old’s problem

Since the old entrepreneur can choose to continue the entrepreneurial activity

or retire, his state variables are his current assets at and his entrepreneurial

ability level θt. His value function is given by

Wt(at, θt+1) = max{W et (at, θt),W

rt (at)}, (12)

where W et (at, θt) is the value function for the old entrepreneur who stays in

business, and W rt (at) is the value function of the old retired person. Define the

inherited assets, net of estate taxes, as ant+1 = at+1 − τ b

t+1 ·max(0, at+1 − et+1).

We have

W et (at, θt) = max

ct,kt,nt,at+1

{u(ct)+βπoEtWt+1(at+1, θt+1)+β(1−πo)EtVt+1(ant+1, yt+1, θt+1)}

(13)

subject to eq. (3), eq. (4), eq. (6), eq. (7), eq. (8) and

u(ct) + βπoEtWt+1(at+1, θt+1) + β(1 − πo)EtVt+1(ant+1, yt+1, θt+1) ≥ W r

t (f · kt).

(14)

The child of an entrepreneur is born with ability level (θt+1, yt+1). The expected

value of the child’s value function with respect to yt+1 is computed using the

invariant distribution of yt, while the one with respect to θt+1 is conditional

on the parent’s θt and evolves according to the same Markov process that each

person faces for θt while alive. This is justified by the assumption that the

child of an entrepreneur inherits the parent’s firm.

A retired person (who is not an entrepreneur) receives pensions and social

17

security payments (pt) and consumes his assets. His value function is

W rt (at) = max

ct,at+1

{u(ct)+βπoWrt+1(at+1)+β(1−πo)EtVt+1(a

nt+1, yt+1, θt+1)} (15)

subject to eq. (6) and

at+1 = (1 + rt)at + pt − Twt (pt + rtat) − (1 + τ c

t )ct. (16)

The expected value of the child’s value function is taken with respect to the

invariant distribution of yt and θt.

3.7 Equilibrium definition

Let xt = (at, yt, θt, st) be the state vector, where s distinguishes young workers,

young entrepreneurs, old entrepreneurs, and old retired. From the decision

rules that solve the maximization problem and the exogenous Markov process

for income and entrepreneurial ability, we can derive a transition function

Mt(xt, ·), which provides the probability distribution of xt+1 (the state next

period) conditional on the current state xt.

An equilibrium is given by the following functions

a risk free interest rate rt and wage rate wt,

taxes (Twt (.), T e

t (.),τ ct , τ b

t , et) and social security payments pt,

allocations ct(x), and at(x), occupational choices,

entrepreneurial labor hiring nt(x), and investments kt(x),

and a distribution of people over the state variables xt: mt(x),

such that, given rt, wt, and government taxes and transfer schedules:

18

• The functions ct, at, nt and kt solve the maximization problems described

above.

• The capital and labor markets clear. Total labor supplied by the work-

ers equals the total labor employed in the non-entrepreneurial sector

and total labor hired by the entrepreneurs. Total household savings in

the economy equal the sum of the total capital employed in the non-

entrepreneurial and entrepreneurial sectors plus government debt.

• The marginal product of labor and the marginal product of capital (net

of depreciation) in the non-entrepreneurial sector are equal to wt and rt.

• The government budget constraint balances at every period: total taxes

collected equal government purchases, transfers, and interest payments

on government debt,

∫

(T xt (Yx)+τ c

t c(x)+Io(x)τ bt (1−πo)·max(0, at+1(xt)−et))dmt(x) = ptπr+gt+rtDt.

The integral is over all of the population, Io is an indicator function that

is equal to one if the person is old and zero otherwise, and πr is the

fraction of retired people in the population. In steady state Dt = D.

• The distribution of people mt is induced by the transition matrix of the

system as follows

m′

t+1 = Mt(xt, ·)′m(t)′.

In steady state mt = m∗ is the invariant distribution for the economy and

debt, prices, and government policies are constant and the individual’s

decision rules are time-independent.

19

3.8 The transition path between steady states

Our economy starts from an initial steady state in which there is estate tax-

ation. Unexpectedly, the government abolishes estate taxes and makes up for

the shortfall of government revenues by changing one of the following three

instruments:

1. government spending,

2. the consumption tax,

3. the proportional part of the tax on total income.

When we use either the income or the consumption tax, we allow the

government to adjust this policy instrument for ten years, and after this period

the tax is set at its final steady state level. The level of the tax during these

years is determined by the requirement that the government budget constraint

has to be satisfied in present value. The shape of the tax change over this time

period is constrained to be piecewise linear over two five-years subperiods.

That is, during these ten years the government could, for example, raise the

chosen tax instrument for five years, and then lower it down to its final steady

state value for other five years. In these experiments government expenditure

is kept fixed as a fraction of total output both during the transition and in the

final steady state.

For all final steady states we set government debt to be the same constant

fraction of total output as in the initial steady state.

When we change government spending as a result of the abolition of the

estate tax, we keep all other tax rates fixed at their initial steady state value,

and we take government debt to be a constant fraction of output also during

20

the transition path. Budget balance for the government then implies how much

government expenditure is.

As soon as people learn about the new policy, the households reoptimize

their behavior taking as given the new path of government policy and prices.

Barring any other changes, the economy will eventually settle down on a final

steady state as a result of the new tax code (the final steady state). During

the intervening years, the economy will be in a transition.

The transition will take longer than the period over which taxes change

because the distribution of people over state variables will take a while to

reach its steady state level, and because of general equilibrium effects (the

prices will take a while to get close to their steady state levels).

4 Calibration

Tables 1 and 2 list the parameters of the model. Table 1 lists the parameters

that we take as given and do not use to match model-generated moments with

moments in the data. Table 2 lists the parameters of the model that we choose

so that the data generated by the initial steady state of the model matches

some relevant counterpart of the observed data.

Regarding the first set of parameters, we take the coefficient of relative

risk aversion to be 1.5, a value close to those estimated, among others, by

Attanasio et al. [6]. As is standard in the business cycle literature, we choose

a depreciation rate δ of 6% and the capital share in the non-entrepreneurial

production function of .33. The probability of aging and of death are such

that the average length of the working life is 45 years and the average length

of the retirement period is 11 years. This implies that the fraction of young

people in the population is about 80%. The logarithm of the income y process

21

for working people is assumed to follow an AR(1). We take its persistence to

be .95, as estimated, for instance, by Storesletten et al. [44]. The variance is

chosen to match the Gini coefficient for earnings of .38, the average found in

the PSID. We assume that the income process and the entrepreneurial ability

processes evolve independently; the exact values for the income and ability

processes are described in Appendix A. The social security replacement rate

is 40% of average gross income. (see Kotlikoff et al. [29].)

The average of the ratio between government purchases and GDP over

1990-99 was 18.7% (Economic Report of the President, 2000).

As in Altig et al. [4], we take the tax rate on consumption to be 11%. The

ratio of total indirect taxes to personal consumption expenditure in the NIPA

accounts has been quite stable around 11%-12% from 1989 to 1999.

We pick the level of government debt (as a fraction of output) so that,

given the equilibrium interest rate, every period the total interest payments

on government debt equal 3% of output (as in Altig et al. [4]).

We estimate the parameters of the tax function on total income using PSID

data for 1989. See Appendix B for details. Figure 1 displays our estimated

average tax rates as a function of total income for the whole population and

for the subpopulations of entrepreneurs and workers.

In previous work (Cagetti and De Nardi [11]) we have discussed the relevant

empirical counterpart to the entrepreneur in our model. We have argued that

our entrepreneurs are the self-employed business owners that actively manage

their own firm(s). We identify them in the Survey of Consumer Finances (SCF)

with those that declare that they are self-employed, that they own a business,

and that they actively manage it.

Table 2 lists the remaining parameters of the model and their correspond-

ing values in the baseline calibration. We consider only two values of en-

22

Parameter Value Source(s)Preferences, technology, and demographics

σ 1.5 Attanasio et al. [6]δ .06 Stokey and Rebelo [43]α .33 Gollin [22]A 1 normalizationπy .98 average working life: 45 yearsπo .91 average retirement life: 11 years

Labor income process and social security paymentsy, Py see appendix A Huggett [25], Lillard et al. [31]

p 40% average yearly income Kotlikoff et al. [29]Public expenditure, government debt, and taxes

g 18.7% GDP NIPAD see text Altig et al. [4]τc 11% Altig et al. [4]bw .32 our estimatesbe .26 our estimatessw .22 our estimatespw .76 our estimatespe 1.4 our estimatesse .42 our estimates

Table 1: Fixed parameters and their sources.

23

0 200 400 600 800 10000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Total income (thousands of dollars)

Ave

rage

tax

rate

PopulationWorkersEntrepreneurs

Figure 1: Estimated average tax rates for the whole population, workers, andentrepreneurs.

trepreneurial ability: zero (no entrepreneurial ability) and a positive number.

This implies that Pθ is a two-by-two matrix. Since its rows have to sum to

one, this gives us two parameters to calibrate. We also have to choose values

for ν, the degree of decreasing returns to scale to entrepreneurial ability, γ,

the share of income going to entrepreneurial working capital, f , the fraction of

working capital the entrepreneur can keep in case he defaults, the estate tax

rate, and its corresponding exemption level.

In total, these are nine parameters to be used to match nine moments of

the data. We use the first seven to target the following moments generated by

the model: the capital-output ratio (3.0), the fraction of entrepreneurs in the

population (7.6 percent), the fraction of entrepreneurs exiting entrepreneur-

ship during each period (22%), the fraction of workers becoming entrepreneurs

during each period (2.5%), the ratio of median net worth of entrepreneurs to

that of workers (7), the fraction of people with zero wealth (7-13%), the frac-

tion of entrepreneurs hiring workers on the labor market (60%). We choose the

other two parameters to match the revenue from estate and gift taxes (0.3%

of output) and the fraction of the estates that pay estate taxes (2%). Our

24

CalibratedParameter Value

β .9θ [0, 0.6]Pθ see textν .88γ .84f 75%τb 16%e 120

Table 2: Calibrated parameters.

calibration matches all of these targets well.

While our calibrated share of income that goes to entrepreneurial working

capital might appear high compared to the one that people use in the aggregate

economy (.33-0.40), it should be noted that this high number is necessary to

match the empirical observation that 40% of entrepreneurs hire no labor on

the market.

5 Results: evaluating our model generated data

against the actual data.

We now compare some important features of the actual data for the U.S.

economy with the corresponding features of our model-generated data. A good

fit of the model to aspects of the data that were not matched by construction in

our calibration procedure increases our faith in the policy projections generated

by the model.

25

5.1 Wealth distribution

Table 3 compares some data for the U.S. economy (from the 1989 SCF, the

data from other years are similar) and for the model-generated data, and

Figures 2 and 3 compare the wealth distribution for the same U.S. data and

for the model, respectively, for the whole population and for the subpopulation

of entrepreneurs.

Our framework with entrepreneurial choice fits the observed wealth distri-

bution very well, both for the whole population, and for the subpopulation of

the entrepreneurs. See Cagetti and De Nardi [11] for a discussion on the role

of entrepreneurship in shaping wealth concentration, on the relationship be-

tween borrowing constraints and entrepreneurial entry, and on entrepreneurial

returns.

0 1000 2000 3000 4000 50000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Positive wealth, in thousands of dollars

Frac

tion

of p

eopl

e

Figure 2: Distribution of wealthfor the whole population. Dash-dot line: data; solid line: baselinemodel.

0 1000 2000 3000 4000 50000

0.02

0.04

0.06

0.08

Positive wealth, in thousands of dollars

Frac

tion

of p

eopl

e

Figure 3: Distribution of the en-trepreneurs’ wealth. Dash-dot line:data; solid line: baseline model.

26

Percentage wealth in the topWealthGini 1% 5% 20% 40%

U.S. data .78 30 54 81 95Model .82 30 60 85 95

Table 3: Baseline calibration.

5.2 Wealth mobility

To evaluate the policy implications of the model it is also important to evaluate

whether the dynamics of the model are consistent with those in the observed

data. Given that wealth is our main interest, we evaluate here the wealth

dynamics of the model.

Unfortunately the SCF, which is the data set specifically designed to study

wealth and the behavior of the wealthy (see Cagetti and De Nardi [12] for

a discussion on this point) does not have a panel dimension. Hence, it can-

not be used to study wealth dynamics at the household level. We therefore

use data from the wealth supplement of the Panel Study of Income Dynamics

(PSID), which does have a panel dimension, and also asks questions that al-

low us to distinguish the self-employed business owners from the workers. The

PSID wealth supplement is available every five years. We report the transi-

tion dynamics for the 1989-1995 period (the results from the other years look

similar).

To understand the relationship between mobility and occupational choice,

we follow the same approach followed by Quadrini ( [36] and [37]). We compute

net worth terciles for the whole population of both self-employed business own-

ers and workers. We divide the population according to occupational mobility

27

as follows: workers that remain workers, workers that become entrepreneurs,

entrepreneurs that remain entrepreneurs, and entrepreneurs that switch to be-

ing workers. For each of these subcategories we compute wealth mobility across

net worth terciles.

Table 4 reports both the results and the number of observations corre-

sponding to each cell. We can see that in our sample the total number of

workers that remain workers is 2214, the total number of workers that switch

to being entrepreneurs is 75, the total number of entrepreneurs that switch to

being workers is 49, and the number of entrepreneurs that stay entrepreneurs

is 206. These numbers are important because they highlight how some of the

transition matrices are based on a small number of observations and should

therefore be taken with caution.

This said, the transition matrices indicate more wealth upward mobility

for the entrepreneurs that stay entrepreneurs than for the workers that stay

workers. Although the mobility matrices off the main diagonal (workers to en-

trepreneurs and entrepreneurs to workers) are based on a very small a sample

size, they seem to broadly indicate that the workers that become entrepreneurs

are more upwardly mobile than those that remain workers, and that the en-

trepreneurs that switch to being workers are more downward mobile than those

that remain entrepreneurs.

We compute the analogous occupation and wealth mobility transition ma-

trix generated by our model (also over a five year period). The results are in

table 5. The transition matrices estimated using our model include all of the

population, and therefore do not have a small sample problem.

Table 5 shows that our model matches extremely well the wealth transitions

of the workers to workers (the one for which the PSID has more observations),

and that also matches quite well the important patterns of the PSID data that

28

Staying workers Switching workers0.79 0.18 0.03 0.47 0.44 0.080.21 0.64 0.15 0.04 0.42 0.540.02 0.23 0.75 0.00 0.23 0.77

number of observations for each cell661 148 29 17 16 3163 507 115 1 11 1416 135 440 0 3 10

Switching entrepreneurs Staying entrepreneurs0.75 0.25 0.00 0.50 0.33 0.170.20 0.70 0.10 0.21 0.51 0.280.06 0.29 0.65 0.02 0.07 0.91

number of observations for each cell6 2 0 6 4 22 7 1 9 22 122 9 20 3 10 138

Table 4: Wealth mobility: data from the PSID 1989 to 1994.

we have discussed above, such as more upward mobility for the entrepreneurs,

and for the workers that become entrepreneurs.

5.3 Consumption inequality

Table 6 reports data from the consumption distribution in the United States3

and in our benchmark model economy. The first row displays the U.S. distri-

bution of consumption of non-durable goods, while the second row reports the

U.S. distribution of consumption of non-durable goods plus imputed services

of consumer durables. These two lines show that these distributions are very

3Data from the 1991 wave of the Consumer Expenditure Survey (CEX). Computationsby Castaneda et al. [13].

29

Staying workers Switching workers0.76 0.23 0.01 0.16 0.60 0.240.22 0.58 0.20 0.01 0.28 0.710.00 0.21 0.79 0.00 0.01 0.99Switching entrepreneurs Staying entrepreneurs0.38 0.45 0.17 0.03 0.14 0.830.08 0.42 0.50 0.02 0.08 0.920 0.03 0.97 0.00 0.01 0.99

Table 5: Wealth mobility: model.

Top groupsEconomy 1% 5% 10%

US (ND+) 4% 14% 24%US (ND) 5% 15% 25%

Benchmark (C96) 5% 18% 29%Benchmark (C99) 8% 26% 38%

Benchmark 16% 36% 46%

Table 6: Consumption distribution: data and model.

similar.

The third and fourth row of table 6 report the same statistics for the

data generated by our benchmark economy when we respectively eliminate

the wealthiest 4% and 1% of the model economy households from the sample,

while the last row displays the consumption statistics for the whole sample.

The large differences in these distributions highlight the extreme sensi-

tivity of the inequality statistics to the lack of oversampling of the richest

households and to the amount of top-coding (a point discussed by Davies and

Shorrocks [16] in the context of the wealth distribution). Consumption is mea-

30

sured with significant measurement error even in the CEX, which is the best

data set for household-level consumption for the United States. For exam-

ple, if one aggregates the consumption CEX data, the CEX underestimates

consumption by 35% compared to National Income and Products Accounts

(NIPA). On these points see Slesnick [42], and more recently, Attanasio, Bat-

tistin and Ichimura [7].

Given the problems with the consumption data sets, and given how well

a mismeasured consumption distribution from our model fits the data, we

consider this check as additional evidence of the validity of our model and its

calibration.

6 Abolishing estate taxation

For each policy we first discuss the long-run outcomes, we then describe the

transition path to the new steady state, and we finally analyze the welfare

costs and benefits.

The welfare costs and benefits are expressed in terms of the fraction of

consumption needed to have someone indifferent between the new and the old

tax system, taking the whole transition path into account. Positive numbers

indicate gains from the tax reform. The horizontal axis represents one’s net

worth at the moment the reform is announced. The solid line is the cumulative

distribution of either young or old people people at the time of the announce-

ment of the reform. The scale for this variable is on the right-hand side of the

graph. The other two lines display the welfare gain or loss for a person with

the middle ability level as a worker and, respectively, the lowest ability level as

an entrepreneur (dashed line) and the highest ability level as an entrepreneur

(dash-dot line). For all policy experiments, the welfare costs and benefits for

31

workers of other ability levels are very similar to the ones that reported.

K Y Interest Perc. Perc. wealth held by toprate Entr. 1% 5% 10% 20%

Benchmark economy9.02 3.00 3.33% 7.6 29.5 59.5 73.6 85.4

No estate tax, lower g

+2.4% +1.3% 3.14% 7.6 30.5 60.6 74.2 85.8No estate tax, higher τc

+2.7% +1.4% 3.12% 7.6 30.5 60.6 74.2 85.8No estate tax, higher τs

+.8% +0.1% 3.22% 7.6 30.4 60.3 74.0 85.7

Table 7: Abolishing the estate tax and adjusting another policy instrument,comparing initial and final steady states.

6.1 Abolishing estate taxation and adjusting govern-

ment purchases

Government purchases are unproductive in this framework. It is therefore

unsurprising that in the model economy (see Table 7, line 2) cutting the estate

tax at the expense of government purchases raises total output (by 1.3%)

and capital (by 2.4%). The interesting finding here is that this effects are

substantial when compared to the small revenue coming from the estate tax.

The elimination of the estate tax increases output by a factor of four times

the revenue raised by the estate tax, and raises capital by at least a factor

of eight. Abolishing estate taxation benefits the newborn entrepreneurs, who

inherit larger estates and can run larger firms and make money more quickly

as a result. More funds in the economy are thus invested in the more produc-

32

Perc. consumption by top1% 5% 10% 20%Benchmark economy16.1 35.5 46.1 59.4No estate tax, lower g

16.7 36.1 46.6 59.7No estate tax, higher τc

16.7 32.6 46.7 59.8No estate tax, higher τs

16.5 35.9 46.3 59.6

Table 8: Abolishing the estate tax and adjusting another policy instrument,consumption distributions, comparing initial and final steady states.

tive technology, the entrepreneurial one. This increase in investment is further

amplified by the reduction in the interest rate, which represents the opportu-

nity cost of funds for the entrepreneurs. This price change benefits all of the

entrepreneurs.

Despite the resulting increases in investment, capital, and output, the gov-

ernment revenues from consumption and income taxes are not enough to make

up from the shortfall in government revenues due to the abolition of the es-

tate tax, and the government has to cut government purchases as a fraction

of output as a result. However, while the revenue from estate taxes in initial

steady state is 0.3% of output, the government has to cut spending only by

0.05% as a fraction of output (with respect to the initial steady state) because

of the increase in output (and thus tax revenues) generated by the abolition

of estate taxes.

Another interesting finding from this experiment is that abolishing estate

taxation changes long-run consumption and wealth inequality very little. Ta-

33

ble 8 reports the consumption distributions.

10 20 30 40 50 60 70

11.5

11.55

11.6

11.65

11.7

Time

Cap

ital

Figure 4: Total capital over time after eliminating estate taxes and reducinggovernment spending.

Figure 4 plots the path of total capital in the economy starting from the

initial steady state and transiting to the final steady state of the economy.

When the estate tax is eliminated and government spending is cut accordingly,

total capital increases for about 50 years. Aggregate output follows a very

similar path.

Figures 5 and 6 display the welfare gains and losses (expressed as a fraction

of yearly consumption) from switching to the economy with no estate taxes

and reduced government spending.

The solid line represents the cumulative distribution of either the young

or the old people at the time of the reform. This line, together with the

consumption compensation lines, shows that almost 80% of the young and

over 90% of the old benefit from this reform. The young make up for 80% of

the population.

Who gains from this reform? The largest gains are experienced by the old,

and especially by the rich among them, but people in the lower-middle class

(defined as having net worth below half a million dollar) also benefit.

34

Those that are very rich, and especially the old among them, benefit from

the break in estate taxation. The immensely rich old experience a consumption

gain of 7%, while the gain of their young counterparts is less than 1%. This

is because the old are much closer to the time of their demise, and thus value

the estate tax break more. (The scales at the left of each of the two graphs

refer to the consumption compensation.)

Those whose net worth is below half a million dollars gain because of the

increase in wages resulting from more aggregate capital accumulation. For

them, wage income makes up for most of total income.

The losers are the young that are not poor enough and not rich enough:

those whose net worth is above half a million dollar, but below ten or twenty

(depending on their entrepreneurial ability level). This is because capital in-

come makes up for a large share of their total income, and the interest rate

drops as a result of this reform.

Similarly, the old with low entrepreneurial ability and assets above 1 million

dollar, but below 7 million dollar, are hurt by the decrease in the interest rate.

They also do not benefit from the estate tax break, given that they were below

the exemption level, or close to it, before the reform took place.

The average welfare gain from this reform is of the order of 0.2% of yearly

consumption.

6.2 Abolishing estate taxation while adjusting the con-

sumption tax

The consumption tax hike needed to make up from the shortfall in revenues

in the final steady state is small: this tax increases from 11% to 11.3%.

Tables 7 and 8 show that the long-run effects of this reform are very similar

35

0 0.01 0.1 0.5 1 10 20 25−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

Wel

fare

gai

n fo

r th

e yo

ung

Low θHigh θ

0 0.01 0.1 0.5 1 10 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Wealth (millions)

Cum

ulat

ive

dist

ribut

ion

of y

oung

Figure 5: Welfare gains of elim-inating estate taxes and reducinggovernment spending for the initialyoung.

0 0.01 0.1 0.5 1 10 20−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Wel

fare

gai

n fo

r th

e ol

d

Low θHigh θ

0 0.01 0.1 0.5 1 10 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Wealth (millions)

Cum

ulat

ive

dist

ribut

ion

Figure 6: Welfare gains of elim-inating estate taxes and reducinggovernment spending for the initialold.

to the ones in the reform in which government spending is cut. Capital and

output increase by similar amounts and wealth and consumption inequality

change little. The fraction of entrepreneurs also remains unchanged.

Figure 7 plots the implied path of the tax rate on consumption over time.

During the transition period the consumption tax peaks at 11.5% before de-

clining to its final steady state level of 11.3%. Figure 3 highlights that capital

overshoots its final steady state level a little bit during the transition, but that

50 years after the policy reform has taken place the majority of the transition

in capital accumulation has occurred. Aggregate output behaves similarly to

aggregate capital.

Figures 9 and 10 report the consumption compensations for this reform.

Even the largest losses are smaller than 1% of yearly consumption. Nonethe-

less, most people lose from switching to this tax system: they are not rich

enough to benefit from the estate tax break, and they have to pay higher con-

sumption taxes. A young person has to own at least fifteen to twenty million

dollars (depending on their entrepreneurial ability) to benefit from the tax re-

36

20 40 60 80 100 1200.11

0.111

0.112

0.113

0.114

0.115

Time

Con

sum

ptio

n ta

x

Figure 7: Consumption tax overtime when eliminating estate taxesand increasing consumption taxes.

20 40 60 80 100 120

11.5

11.55

11.6

11.65

11.7

11.75

Time

Cap

ital

Figure 8: Total capital over timewhen of eliminating estate taxesand increasing consumption taxes.

form, and even for the very richest young people the benefits are small. Many

of the elderly are also hurt by the reform, given that they must hold four to ten

million dollar (depending on the ability level) to benefit from the tax reform.

The benefits for the very rich, however, are significant: on the order of almost

7% of yearly consumption.

The average welfare cost from this reform is of the order of 0.3% of con-

sumption.

6.3 Abolishing estate taxation while adjusting the pro-

portional income tax

To balance the government budget constraint, the proportional part of the

income tax increases from 3.6% to 4.0%. This change affects all of the house-

holds in the economy and, in particular, decreases the return (net of taxes)

from investing in capital for the entrepreneurs. The entrepreneurs hit more

harshly by this tax increase are most of the young ones (for which the expected

37

0 0.01 0.1 0.5 1 10 20 25−0.02

−0.015

−0.01

−0.005

0

0.005

0.01

Wel

fare

gai

n fo

r th

e yo

ung

Low θHigh θ

0 0.01 0.1 0.5 1 10 20 250

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Wealth (millions)

Cum

ulat

ive

dist

ribut

ion

of y

oung

Figure 9: Welfare gains for theinitial young of eliminating estatetaxes and increasing consumptiontaxes.

0 0.01 0.1 0.5 1 10 20−0.02

−0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Wel

fare

gai

n fo

r th

e ol

d

Low θHigh θ

0 0.01 0.1 0.5 1 10 200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Wealth (millions)

Cum

ulat

ive

dist

ribut

ion

Figure 10: Welfare gains for the ini-tial old of eliminating estate taxesand increasing consumption taxes.

time of death is still far in the future, and thus the benefits from the elimina-

tion of the estate tax are small) and the old ones who are not rich enough to

really benefit from the abolition of the estate tax. As a result, there is only a

very small increase in output with respect to the initial steady state, and the

aggregate gains are much smaller compared to the ones in the previous two

reforms.

The long-run effects of this policy on consumption and wealth inequality

are very modest as in the other policies that we have considered.

Castaneda, Dıaz-Gimenez, and Rıos-Rull [13] analyze the effects of a similar

reform in a model with no entrepreneurial choice, in which the key force driving

wealth inequality is that the rich are subject to very large idiosyncratic earnings

shocks (which are calibrated to match inequality in wealth holdings). As in

our model, they find that the abolition of the estate tax generates only a

small increase in wealth inequality. Compared to us, they obtain a long-run

aggregate increase of 0.4% for output, which is four times larger than what

we obtain, and a somewhat larger effect on total capital accumulation (0.87%

38

compared to 0.78%). The additional channel at work in our framework is the

disincentive effect on entrepreneurial investment due to the higher income tax.

Since in our framework the entrepreneurial technology is much more productive

than the non-entrepreneurial one, smaller investment by the entrepreneurs

results in much lower aggregate income than smaller investment by the workers.

Laitner [30] also studies the effects of a similar reform. He adopts a more

stylized economy in which some household are altruistic while others do not

care about their descendants. His main message is that, in his framework,

abolishing the estate tax generates a significant increase in the share of total

net worth held by the richest 1%, while the effects on the aggregates are

relatively small for most parameterizations, but can be positive or negative

depending on the fraction of altruistic households.

In our framework the consumption compensations required by this reform

are similar to the ones that we reported when the consumption tax is raised.

As in that policy, increasing the income tax to make up from lost revenues

from the estate tax implies small welfare losses for most of the population.

The average welfare cost for this reform is of the same order of magnitude

than when the consumption tax is raised.

In sum, we find that eliminating the estate tax while increasing the tax on

total income would generate a small increase on aggregate capital but would

have negligible effects on aggregate output. This reform would slightly increase

wealth inequality, and would redistribute from the young to the old and from

most people to a tiny fraction of rich people, thus generating welfare losses for

the most of the population.

39

7 Conclusions

Our model suggests that eliminating the estate tax would not generate large

increases in wealth and consumption inequality, and increases in aggregate

output and capital accumulation.

Unfortunately, these reforms would also imply welfare losses to the vast

majority of the population, and benefit only the very rich and, in particular,

the old among the very rich.

This happens despite the fact that our framework models explicitly en-

trepreneurial activity and borrowing constraints, which seem to be the key

features that the proponent of abolishing estate taxation are most concerned

about.

There are features of reality that could provide additional reasons to abolish

estate taxation. For example, our model does not consider tax avoidance costs.

Significant amounts of resources might be spent to decrease the tax burden,

through the use of lawyers and accountants. The cost of tax avoidance might

generate a deadweight loss that should be considered in the overall evaluation

of any change in the estate tax. (See Aaron and Munnell [2] and Schmalbeck

[40] for a discussion of the avoidance costs.) This is an important and to a

large extent unexplored issue that we leave for future research.

40

References

[1] Henry J. Aaron and William G. Gale, editors. Economic Effects of Fundamental Tax

Reform. Brookings Institution Press, Washington, D.C., 1996.

[2] Henry J. Aaron and Alicia H. Munnell. Reassessing the role for wealth transfer taxes.National Tax Journal, 45(2):119–143, June 1992.

[3] Rui Albuquerque and Hugo A. Hopenhayn. Optimal dynamic lending contracts withimperfect enforceability. Review of Economic Studies, 71(2):285–315, April 2004.

[4] David Altig, Alan J. Auerbach, Laurence J. Kotlikoff, Kent A. Smetters, and JanWalliser. Simulating fundamental tax reform in the United States. American Economic

Review, 91(3):574–595, June 2001.

[5] David Altig and Charles T. Carlstrom. Marginal tax rates and income inequality in alife-cycle model. American Economic Review, 89(5):1197–1215, December 1999.

[6] Orazio P. Attanasio, James Banks, Costas Meghir, and Guglielmo Weber. Humps andbumps in lifetime consumption. Journal of Business and Economic Statistics, 17(1):22–35, January 1999.

[7] Orazio P. Attanasio, Erich Battistin, and Hidehiko Ichimura. What really happened toconsumption inequality in the us? In Ernst R. Berndt and Charles M. Hulten, editors,Hard to Measure Goods and Services: Essays in Honor of Zvi Griliches. University ofChicago Press, Forthcoming.

[8] Jacob Mikov Barry W. Johnson and Martha Britton Eller. Elements of federal estatetaxation. In Gale et al. [17], pages 65–107.

[9] Olivier J. Blanchard. Debt, deficits, and finite horizons. Journal of Political Economy,93(2):223–247, April 1985.

[10] W. Elliott Brownlee. Historical perspective on historical tax policy towards the rich.In Slemrod [41], pages 29–73.

[11] Marco Cagetti and Mariacristina De Nardi. Entrepreneurship, frictions, and wealth.Journal of Political Economy, 114(5):835–870, October 2006.

[12] Marco Cagetti and Mariacristina De Nardi. Wealth inequality: Data and models.Macroeconomic Dynamics, 2006. Forthcoming.

[13] Ana Castaneda, Javier Dıaz-Gimenez, and Jose-Victor Rıos-Rull. Accounting for theU.S. earnings and wealth inequality. Journal of Political Economy, 111(4):818–857,August 2003.

[14] Juan Carlos Conesa and Dirk Krueger. On the optimal progressivity of the income tax.Journal of Monetary Economics, 53(7), 2006.

[15] Thomas Cooley, Ramon Marimon, and Vincenzo Quadrini. Aggregate consequences oflimited contract enforceability. Journal of Political Economy, 112(4):817–847, August2004.

41

[16] James B. Davies and Anthony F. Shorrocks. The distribution of wealth. In A.B.Atkinson and F. Bourguignon, editors, Handbook of Income Distribution, pages 605–675. Elsevier, Amsterdam, The Netherlands, 2000.

[17] William G. Gale, James R. Hines, Jr., and Joel Slemrod, editors. Rethinking Estate

and Gift Taxation. Brookings Institution Press, 2001.

[18] William G. Gale and Maria G. Perozek. Do estate taxes reduce saving? In Gale et al.[17], pages 216–247.

[19] William G. Gale and Joel Slemrod. Overview. In Gale et al. [17], pages 1–64.

[20] William M. Gentry and R. Glenn Hubbard. Entrepreneurship and household savings.Advances in Economic Analysis and Policy, 4(1), 2004. Article 1.

[21] Mark Gertler. Government debt and social security in a life-cycle economy. Carnegie-

Rochester Conference Series on Public Policy, 50:61–110, June 1999.

[22] Douglas Gollin. Getting income shares right. Journal of Political Economy, 110(2):458–474, April 2002.

[23] Miguel Gouveia and Robert P. Strauss. Effective federal individual income tax func-tions: An exploratory empirical analysis. National Tax Journal, 47(2):317–339, June1994.

[24] Neil E. Harl. Does farm and ranch property need a federal estate and gift tax break?Tax Notes, 67:875–877, August 1995.

[25] Mark Huggett. Wealth distribution in life-cycle economies. Journal of Monetary Eco-

nomics, 38(3):469–494, December 1996.

[26] Timothy J. Kehoe and David K. Levine. Debt-constrained asset markets. Review of

Economic Studies, 60(4):865–888, October 1993.

[27] Sagiri Kitao. Entrepreneurship, taxation, and capital investment. Review of Economic

Dynamics, 2007. forthcoming.

[28] Wojciech Kopczuk and Joel Slemrod. The impact of the estate tax on wealth accumu-lation and avoidance behavior. In Gale et al. [17], pages 299–349.

[29] Laurence J. Kotlikoff, Kent A. Smetters, and Jan Walliser. Privatizing Social Securityin the United States: Comparing the options. Review of Economic Dynamics, 2(3):532–574, July 1999.

[30] John Laitner. Inequality and wealth accumulation: Eliminating the federal gift andestate tax. In Gale et al. [17], pages 258–292.

[31] Lee A. Lillard and Robert J. Willis. Dynamic aspects of earning mobility. Econometrica,46(5):985–1012, September 1978.

[32] Albert Marcet and Ramon Marimon. Communication, commitment and growth. Jour-

nal of Economic Theory, 58(2):219–249, December 1992.

42

[33] Brian Erard Martha Britton Eller and Chih-Chin Ho. Elements of federal estate taxa-tion. In Gale et al. [17], pages 375–410.

[34] Cesaire Meh. Entrepreneurship, wealth inequality, and taxation. Review of Economic

Dynamics, 8(3):688–719, July 2005.

[35] James M. Poterba. The estate tax and after-tax investment returns. In Slemrod [41],pages 333–353.

[36] Vincenzo Quadrini. The importance of entrepreneurship for wealth concentration andmobility. Review of Income and Wealth, 45(1):1–19, March 1999.

[37] Vincenzo Quadrini. Entrepreneurship, saving, and social mobility. Review of Economic

Dynamics, 3(1):1–40, January 2000.

[38] Vincenzo Quadrini and Jose-Victor Rıos-Rull. Models of the distribution of wealth.Federal Reserve Bank of Minneapolis Quarterly Review, 21(2):1–21, Spring 1997.

[39] Vincenzo Quadrini and Jose-Victor Rıos-Rull. Understanding the U.S. distribution ofwealth. Federal Reserve Bank of Minneapolis Quarterly Review, 21(2):22–36, Spring1997.

[40] Richard Schmalbeck. Avoiding federal wealth transfer taxes. In Gale et al. [17], pages113–158.

[41] Joel B. Slemrod, editor. Does Atlas Shrug? The Economic Consequences of Taxing the

Rich. Harvard University Press, Cambridge, 2000.

[42] Daniel T. Slesnick. Aggregate consumption and saving in the United States. Review of

Economic and Statistics, 74:585–597, 1992.

[43] Nancy L. Stokey and Sergio Rebelo. Growth effects of flat-rate taxes. Journal of

Political Economy, 103(3):519–550, June 1995.

[44] Kjetil Storesletten, Chris Telmer, and Amir Yaron. Risk sharing over the life cycle:Genes or luck in the labor market. Mimeo, July 1999.

[45] George Tauchen and Robert Hussey. Quadrature-based methods for obtaining approx-imate solutions to nonlinear asset pricing models. Econometrica, 59(2):371–396, March1991.

[46] Edward N. Wolff. Commentary on Douglas Holtz-Heakin: The uneasy case for abol-ishing the estate tax. Tax Law Review, 51(3):517–521, 1996.

43

A Income and entrepreneurial ability

We assume that the income process is AR(1) and approximate it with a five-

point discrete Markov chain, using the method described in Tauchen and

Hussey [45]. The gridpoints y for the income process (normalized to 1) that

we use are[

0.2468 0.4473 0.7654 1.3097 2.3742]

and the transition matrix Py is

0.7376 0.2473 0.0150 0.0002 0.0000

0.1947 0.5555 0.2328 0.0169 0.0001

0.0113 0.2221 0.5333 0.2221 0.0113

0.0001 0.0169 0.2328 0.5555 0.1947

0.0000 0.0002 0.0150 0.2473 0.7376

.

The transition matrix Pθ is given by

.97 .03

.2 .8

.

B Federal tax schedules

We estimate equation (1) using nonlinear least squares. The data are for 1989

and are taken from the Panel Study of Income Dynamics (PSID). We use the

PSID dataset for this part of our analysis because it asks questions that allow

us to classify households as entrepreneurs and non-entrepreneurs, and, until

1989, it also provides computed data on total taxes paid by the respondents.

44

Parameter Point estimate 95% Confidence intervalWhole sample

b .30 .27-.34p .82 .74-.90s .24 .18-.30

Workers onlybw .32 .26-.38pw .76 .68-.85sw .22 .14-.29

Entrepreneurs onlybe .26 .23-.28pe 1.40 1.1-1.7se .42 .30-.54

Table 9: Estimates for the federal average tax rates.

Our measure of total monetary income includes all forms of labor income,

capital income, transfers, and income from entrepreneurial activities. Total

federal taxes paid is the variable computed in the PSID (in our case, V18862

in the 1990 file). The dependent variable in the regression, average tax rate,

is the ratio of federal taxes paid to total monetary income.

To obtain a representative sample, we exclude the poverty and Latino sam-

ples. To obtain the appropriate tax rate for our model (in which the lowest

income level is positive), we also drop all observations with income smaller

than $1,000 or negative taxes paid.

To make the data on entrepreneurs consistent with those that we use from

the SCF data set and the model we employ, we define as entrepreneurs those

who declare to be self-employed and own or have a financial interest in a busi-

45

ness activity and had an income of at least $1,000 from running the business

during the period. The resulting sample of entrepreneurs has very similar char-

acteristics to those from the SCF. Our estimates would be very similar if we

were to assume a somewhat smaller or larger cutoff for the amount of business

income received during the period.

We perform the estimation on three samples: the whole population of

households, including workers and entrepreneurs, the subpopulation of workers

only, and the subpopulation of entrepreneurs only. The estimated values for

the three groups are shown in Table 9 and plotted in Figure 1.

46